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Line $v$ has a slope of $\frac{6}{5}$ . Line $w$ has a slope of $\frac{5}{6}$ . Are line $v$ and line $w$ parallel or perpendicular? $\newline$ Choices: $\newline$ (A) parallel $\newline$ (B) perpendicular $\newline$ (C) neither

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Slopes of parallel and perpendicular lines

Full solution

Q. Line

v

has a slope of

\frac{6}{5}

. Line

w

has a slope of

\frac{5}{6}

. Are line

v

and line

w

parallel or perpendicular?

\newline

Choices:

\newline

(A) parallel

\newline

(B) perpendicular

\newline

(C) neither

Line $v$ vs Line $w$ : Line $v$ slope: $\frac{6}{5}$ . Line $w$ slope: $\frac{5}{6}$ . Are they the same or opposite reciprocals?
Parallel vs Perpendicular: If lines are parallel, their slopes are equal. If perpendicular, their slopes are opposite reciprocals.
Check Opposite Reciprocal: Check if $\frac{6}{5}$ is the opposite reciprocal of $\frac{5}{6}$ . Opposite reciprocal of $\frac{6}{5}$ is $-\frac{5}{6}$ .
Not Perpendicular: Since $\frac{5}{6}$ is not the negative reciprocal of $\frac{6}{5}$ , lines $v$ and $w$ are not perpendicular.
Not Parallel: Since $\frac{6}{5}$ is not equal to $\frac{5}{6}$ , lines $v$ and $w$ are not parallel.
Conclusion: Lines $v$ and $w$ are neither parallel nor perpendicular.

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